It's worth finishing the star map, if only because some of the more rewarding Alerts take place on outer planets.
As to levelling up frames, once you get a bunch of good mods and have them ranked up, ranking up frames and weapons for the umpteenth forma isn't too onerous. For frames and weapons, and in groups, there are a few methods. Starting on Apollodorus, then doing a couple of T1D "xp runs" (as they are advertized in Recruitment), maybe a T2D or T3D after that, and the frame/weapon is ranked, is one method.
A solo method is to do as high-ranked Spy missions as you can - if you can do the three spy things undetected that's a great xp boost, plus all the respawning mobs nets you a fair amount. An affinity booster gives a huge boost (this is how a lot of "pros" do it, the people who do reviews, etc. - either that or Draco, but it's probably impolitic to admit to doing Draco on a youtube stream).
Draco is the thing for weapons though. (Seimini is another popular holiday destination for this purpose.) Grouped, take any weapon into Draco and it will level up to 30 after 4 rounds. The Draco method does require, though, that you have one of the "meta" frames (Trinity and Frost are always the foundation, then for damage Excalibur, Rhino, Nova are usually somewhere in the meta for Draco at the moment AFAIK, another variation is to have Equinox and Banshee), and also that you have the right builds (therefore the right mods) for those frames. Also, it's etiquette to have at least one fully-functional weapon so you can kill stuff if something goes wrong with the smooth functioning of the meta grind (as it sometimes does).
Other than that, for solo weapon levelling, the same method as levelling frames, as above. Note that you get more affinity for a weapon if you have no other weapons equipped.